Discussion
A farmer wants to plant 121 apple trees, 154 banana trees and 198 mango trees in equal rows. Also he wants to make distinct rows of trees (i.e. only one type of trees in one row). The minimum number of rows required are
Answer: C
The minimum number of rows is 43.
Every row must hold the same number of trees, and each count must divide exactly, so the row size must be a common factor; for the fewest rows it must be the highest common factor:
\[ \begin{aligned} 121 &= 11^{2},\ 154 = 2 \cdot 7 \cdot 11 \\ 198 &= 2 \cdot 3^{2} \cdot 11 \Rightarrow \text{HCF} = 11 \end{aligned} \]
\[ \begin{aligned} &\tfrac{121}{11} + \tfrac{154}{11} + \tfrac{198}{11} \\ &= 11 + 14 + 18 = 43 \end{aligned} \]
11 is the number of trees per row, not the number of rows. 41 and 42 do not match any count.
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